In this paper we discuss planar quadrilateral (PQ) nets as discrete models for convex affine surfaces. As a main result, we prove a necessary and sufficient condition for a PQ net to admit a Lelieuvre co-normal vector field. Particular attention is given to the class of surfaces with discrete harmonic co-normals, which we call discrete affine minimal surfaces, and the subclass of surfaces with ...

This study presents an optimization problem for shape design of a 2-D radiant enclosure with transparent medium and gray-diffuse surfaces. The aim of the design problem is to find the optimum geometry of a radiant enclosure from the knowledge of temperature and heat flux over some parts of boundary surface, namely the design surface. The solution of radiative heat transfer is based on the net r...

Radiant floor heating has received increasing attention due to its diverse advantages, especially the energy saving as compared to the conventional dwelling heating system. This paper presents a numerical investigation of airflow and heat transfer in the slot-vented room with the radiant floor heating unit. Combination of fluid convection and thermal radiation has been implemented through the t...

Affine Differential Geometry provides a set of measures invariant under a larger set of transformations compared to rigid motions. This leads to several applications using robust shape descriptors. Although affine invariant operations are already used for surfaces, they do not intend to approximate the definitions of Affine Differential Geometry, which are the basis for further differential inv...

A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the set enjoys uniform coverage over all non-decreasing regression functions. Furthermore, diameter automatically adapts to unknown number pieces true parameter, sense that bounded from above by minimax risk class $k$-piecewise constant The a increasing f...

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‎let $g$ be a locally compact abelian group‎. ‎the concept of a generalized multiresolution structure (gms) in $l^2(g)$ is discussed which is a generalization of gms in $l^2(mathbb{r})$‎. ‎basically a gms in $l^2(g)$ consists of an increasing sequence of closed subspaces of $l^2(g)$ and a pseudoframe of translation type at each level‎. ‎also‎, ‎the construction of affine frames for $l^2(g)$ bas...